Dec 7, 2015

Continuously Varying Traits: Why Height Has No Short Category

Look at a crowd of people and you will not find tall people and short people. You will find a spread. Most people land in the middle, and the tallest are rare. Height is a continuously varying trait.

Blood type works differently. You are either type A, B, AB or O, with no in-between. That is a discontinuous trait. This post explains why biology needs both kinds, and why the continuous ones are the hard ones to study.

Symmetric histogram showing a normal bell-shaped distribution
Plot a continuous trait and you usually get this shape. Most people sit in the middle, and both extremes are rare — Image: Visnut, CC BY-SA 4.0, via Wikimedia Commons

Two Kinds of Variation

Every trait a population shows is one of two kinds. The difference is not how much genes matter. It is how many bits of information you need to describe the person.

A discontinuous trait, also called qualitative, has clear categories with nothing in between. Round or wrinkled pea seeds. Blood group A, B, AB or O. These are usually controlled by one gene, often with several versions of it.

A continuous trait, also called quantitative, has no categories. There is no dividing line between short and medium height, because the difference between one person and the next is tiny. You have to measure, not label.

Discontinuous traitContinuous trait
CategoriesFew and fixedNone
How you measure itCount themMeasure them
Usual causeOne main gene, or twoMany genes, each adding a small amount
Environment mattersLittleA lot
Shape when graphedSeparate barsA bell curve
ExamplesBlood group, pea seed shape, sexHeight, body mass, grain yield, milk yield, skin tone

Where the bell curve comes from

The shape is not an accident. If a trait is the sum of many small independent effects, the middle values are the most likely. The same reason makes a row of coin tosses cluster near the average.

A Galton board, a physical device that drops beads into a bell-shaped pile
A Galton board. Drop a ball down the pins and it lands near the middle more often than the edges — Image: Antoine Taveneaux, CC BY-SA 3.0, via Wikimedia Commons

If a trait is controlled by one gene with two versions, you get bars with gaps. If it is controlled by many genes that each add a bit, you get a smooth curve. This is the simplest test for which kind of trait you are looking at.

How Many Genes Make a Continuous Trait

A polygenic trait is one controlled by many genes at different places in the genome. Each is called a locus. Each one adds a small amount on top of what the others do. That is why the trait runs from one extreme to the other instead of landing in boxes.

The model that fits best is simple. Each locus has a version that adds a little and a version that does not. Count the versions that add, and you have a prediction. This is called additive inheritance.

Human karyotype showing all 46 chromosomes with banded regions marked
A human karyotype. Every band is a region that can hold a locus, and a polygenic trait draws on bands scattered across many of them — Image: Mikael Häggström, CC0, via Wikimedia Commons

Because the effects add up rather than compete, they behave differently from the usual dominant and recessive pattern. If one version of a gene masked another, the trait would fall into a small number of groups. Adding instead of masking is exactly what produces the unbroken range.

Finding the loci

You cannot find these genes by looking for a mutant with an unusual trait. The effects are too small for that. The method used instead is to measure the trait in thousands of people, then look for DNA variants that match the measurements.

A genome-wide association study does this. A quantitative trait locus, or QTL, is any place in the genome where a DNA variant reliably goes up and down with the trait. Finding a QTL is usually the first step toward finding the gene that does the work.

Galton, Regression, and Heritability

The idea that a trait is partly inherited and partly environmental is old. Francis Galton drew it out in 1875, using his own data on the heights of parents and children.

Francis Galton's 1875 diagram of parents' heights against children's heights
Galton's 1875 diagram. Tall parents tend to have tall children, but less extremely so than the parents — Image: Francis Galton, public domain, via Wikimedia Commons
Portrait photograph of Francis Galton
Francis Galton, who measured heights, drew the first plots, and named the effect below — Image: Gustav Graef, public domain, via Wikimedia Commons

Regression to the mean

The pattern in that diagram became its own idea. If both parents are tall, their child is usually tall too, but closer to average than they were. The same works at the other end. Galton called it a constant fraction of the parents' deviation from the middle, and called the effect regression to the mean.

This has a practical consequence that catches people out. If you pick the best-performing sales quarter and pick the best-performing salesperson, both will usually look worse next period. Nothing went wrong. Both were partly lucky to begin with.

Heritability is about a population, not a person

Heritability is the share of the variation in a trait that genetic differences between people in a population account for. The rest comes from the environment and from measurement error.

The important catch is that heritability does not tell you what share of one person's trait came from genes. If a trait has a heritability of 0.6, that does not mean 60 percent of your version of it is inherited. It describes how spread out the group is, not how you are built.

Heritability can also move without any gene changing. If every person in the group eats the same diet, the environment stops explaining any of the differences, and the same measured heritability goes up. In human studies the environment is often split into what people share, such as a household, and what they do not.

Real Traits, Measured Properly

These are the cases where the genetics is well documented, and each one shows the same pattern: many small genetic effects, plus an environment that shifts the whole thing.

Human height

Height is the textbook case. Twin studies put its heritability at 60 to 80 percent. A genome-wide study of more than 180,000 people found hundreds of variants spread across at least 180 loci.

The older textbook claim that shortness is dominant and tallness is recessive is wrong. Height is additive across many loci, so there is no single allele that masks another. Nutrition, illness and childhood conditions all move the result as well. That is why average height in a population has risen over the past century, with no change in the gene pool at all.

Skin color

Skin tone was taught as a simple three-to-six gene trait. That is out of date. Skin color depends mostly on how much melanin the skin makes, and the genes behind it include MC1R, SLC24A5, SLC45A2 and HERC2/OCA2.

A sun-tanned arm next to the untanned skin of the same arm
The environment moves the same trait the genes set up. Sun exposure adds pigment on top of inherited tone — Image: Onetwo1, CC BY-SA 3.0, via Wikimedia Commons
Map showing the geographic distribution of the OCA2 pigmentation allele
One OCA2 variant alone accounts for roughly 8% of the skin tone difference between African and East Asian populations — Image: Lian Deng and Shuhua Xu, CC BY 4.0, via Wikimedia Commons
Map showing the geographic distribution of an MC1R variant across Europe and Africa
MC1R is a different kind of story. It mainly decides whether skin makes the pale pigment or the dark one, not how light or dark the skin ends up — Image: Lian Deng and Shuhua Xu, CC BY 4.0, via Wikimedia Commons

Sun exposure adds to all of this. That is why the same person looks different in summer, and why skin tone is a reaction norm rather than a fixed label.

Body mass and agricultural yield

Body mass index is a good example of a measured trait that gets argued about, because the number sits on a shared scale and moves with the population average.

Standard body mass index chart showing the normal, overweight and obese ranges
A BMI chart is a set of fixed cut-offs drawn on a continuous measurement. Where the lines sit depends on the population — Image: nagualdesign, CC BY-SA 4.0, via Wikimedia Commons

Breeders use the same mathematics on wheat, milk and meat. They cannot breed for a category, because there is no category. They select the people at the top of a measured range, over and over, and the average of the population moves. That is quantitative genetics working exactly as intended.

Line chart showing how wheat yield has changed over time
Wheat yield is breeding done on a number rather than a label. Each generation is selected on the measurement — Image: AndrewMT, CC BY-SA 3.0, via Wikimedia Commons

Genes Set the Range, Environment Sets Where You Land

The cleanest way to say all of this is the reaction norm. It describes how one genotype behaves across a range of environments. The idea was introduced by Richard Woltereck in 1909.

Two plants with the same genes can end up very different sizes if one is short of water and the other is not. Two people with the same height genes can end up at different heights on different diets. The genes set the limits of what is possible. The environment decides where inside those limits each individual lands.

This is why the phrase nature versus nurture is a bad way to think about it. The two are not opponents. They are pulling on the same trait at the same time, and most complex traits need both to explain.

Key Takeaways

  • Discontinuous traits fall into fixed categories. Continuous traits do not, and have to be measured instead of labelled.
  • A continuous trait is usually polygenic: many loci, each adding a small amount.
  • Adding rather than masking is what produces the unbroken range of values.
  • Plot one and you usually get a bell curve. That is what many small effects added together look like.
  • Galton found that extremes do not stay extreme. He called it regression to the mean.
  • Heritability describes how spread out a group is. It does not tell you how much of one person came from genes.
  • Height is 60 to 80% heritable, with hundreds of variants across at least 180 loci. The old dominance claim about it is wrong.
  • Skin color is not a three-gene trait, and the environment moves it too.
  • Genes set the range. Environment decides where inside it you land.

Frequently Asked Questions

Is blood type continuous or discontinuous?

Discontinuous. There are four types and no in-between, because the trait is set by one gene with three main versions. You count blood groups. You never measure them.

Why do most people fall in the middle of a continuous trait?

Because the trait is a sum of many small effects. To be extreme, you need the unusual version at many loci at once. Holding all of them in the same person is unlikely, so the extremes stay rare.

If a trait is heritable, is it fixed by genes?

No. Heritability says how much of the spread in a group is genetic. It says nothing about how changeable an individual is, and the same heritability figure can hold in two groups with very different lives.

Why did average height rise over the past century?

Almost entirely because of environment. Better nutrition, less childhood illness and fewer infections let more people reach the height their genes already allowed. The gene pool did not change on that timescale.

Is eye color a continuous trait?

Older textbooks listed it as one, alongside height. That is now known to be wrong. Eye color turns out to be largely set by a small number of genes. HERC2/OCA2 does much of the work. So it behaves far more like a discontinuous trait than textbooks once described.

Can the environment change a genetic trait permanently?

The environment changes how a gene is used, which is different from changing the gene itself. Some effects do last for life, and some are reversible. Sun tan fades. A childhood shortage of nutrition can limit final height permanently. The reaction norm describes how much room there is between those outcomes.

Sources: Wikipedia articles on quantitative traits, quantitative genetics, polygenic inheritance, heritability, quantitative trait loci, regression to the mean, Francis Galton, the normal distribution, human height, human skin color, melanin, dominance and incomplete dominance, and reaction norm. Images: Wikimedia Commons, with authors and licenses noted in each caption.